Post processing algorithms for distributed optical fiber ...

Post processing algorithms for distributed

optical fiber sensing in SHM applications

Mattia Francesco Bado*

Department of Civil and Environmental Engineering (Technical University of Catalunya. UPC-BarcelonaTech),

Campus Nord, Calle Jordi Girona 1-3, 08034 Barcelona, Spain and Institute of Building and Bridge Structures

(Vilnius Gediminas Technical University), Saulėtekio al. 11, 10221 Vilnius, Lithuania

&

Joan Ramon Casas & Judit Gómez

Department of Civil and Environmental Engineering (Technical University of Catalunya. UPC-BarcelonaTech),

Campus Nord, Calle Jordi Girona 1-3, 08034 Barcelona, Spain

Abstract: Distributed Optical Fiber Sensors (DOFS) are

measuring tools whose potential related to the civil

engineering field has been discovered in the latest years only

(reduced dimensions, easy installation process, lower

installation costs, elevated reading accuracy and distributed

monitoring). Yet, what appears clear from numerous in-situ

DOFS monitoring campaigns (bridges and historical

structures among others) and laboratory confined

experiments, is that OFS monitorings have a tendency of

including in their outputs a certain amount of anomalistic

readings (out of scale and unreliable measurements). These

can be both punctual in nature and spread over all the

monitoring duration. Their presence strongly affects the

results both altering the data in its affected sections and

distorting the overall trend of the strain evolution profiles;

thus the importance of detecting, eliminating and

substituting them with correct values. Being this issue

intrinsic in the raw output data of the monitoring tool itself,

its only solution is a computer-aided post-processing of the

strain data. The present paper discusses different simple

algorithms for getting rid of such disruptive anomalies by

means of two methods previously used in literature and a

novel polynomial based one with different levels of

sophistication and accuracy. The viability and performance

of each is tested on two study case scenarios; an

experimental laboratory test on two reinforced concrete

tensile elements and an in-situ tunnel monitoring campaign.

The outcome of such analysis will provide the reader with

both clear indications on how to purge a DOFS-extracted

data set of all anomalies and on which is the best suited

method according to their needs. This marriage of computer

technology and cutting edge Structural Health Monitoring

tool not only elevates the DOFS viability but provides civil

and infrastructures engineers a reliable tool to perform

previously unreachable levels of accuracy and extension

monitoring coverage.

NOTATION TABLE

Notation Definition

SHM Structural Health Monitoring

OFS Optical Fiber Sensor

DOFS Distributed Optical Fiber Sensor

OBR Optical Backscatter Reflectometer

RC Reinforced Concrete

SRA Strain Reading Anomaly

HL-SRA Harmless Strain Reading Anomaly

HF-SRA Harmful Strain Reading Anomaly

SSQ Spectral Shift Quality

GTM Geometrical Threshold Method

PICM Polynomial Interpolation Comparison Method

1 INTRODUCTION

As clearly stated by Brownjohn1, civil infrastructure

provides the means for a society to function. The wide range

of applications that civil engineering offers includes

buildings, bridges, highways, tunnels, power plants,

industrial facilities, geotechnical and hydraulic structures

among others. Each of these is subjected to multiple events

that deteriorate and compromise its structural integrity in a

unique way throughout its service lifetime exposing its

future performance to several risks. In order to avoid the

social, economic and environmental costs of deterioration

and/or failure, civil structures have different safety and

durability requirements that need to be met and that ensure a

correct structural performance and the wellbeing of their

users. For that, a series of inspection, monitoring and

maintenance protocols have to be carried out during the

structure’s service lifetime.

The effectiveness of these monitoring methods relies in

their ability to rapidly detect alterations on the structure’s

performance, allowing for its identification, characterization

and control. This idea is the basis of Structural Health

Management (SHM), which, according to Housner et al.2,

can be understood as the continuous or regular measurement

and analysis of key structural and environmental parameters

under operating conditions, for the purpose of warning of

abnormal states or accidents at an early stage.

Traditional structural monitoring techniques involve the

use of inclinometers, accelerometers, extensometers, total

station surveys, load cells and GNS-based sensors, among

many others. These tools have a wide applicability and are

quite reliable since their correct deployment is widely

acknowledged, easily ensuring reliable monitoring and,

consequently, structural assessment. However, as stated in

Baker3, conventional forms of inspection and monitoring are

only as good as their ability to uncover potential issues in a

timely manner. Regarding the ability of damage detection,

traditional tools present several drawbacks such as

insufficient data management ability, the need for the

infrastructure’s service interruption during their deployment,

non-automated real-time measures and non-distributed

sensing and more.

Among the most modern monitoring technologies

adopted in the structural engineering field, Optical Fiber

Sensors (OFS), SOFO deformation sensors4, Global

Positioning Systems (GPS), radars, Micro Electro

Mechanical Systems (MEMS) and Image Processing

Techniques are increasingly gaining in popularity. As a

matter of fact, these have opened the doors to the extraction

of structural information that could not be acquired before5,6.

Generally speaking, the structural assessments through

monitoring tools rely essentially on the precision of the

sensors, on its automation level and data management speed.

OFS sensors have recently upped their performance to

embrace these requirements and are the main subject of the

present paper. These sensing tools provide several

advantages regarding SHM given its reduced dimensions,

easy installation process, lower maintenance, lower

installation costs, reading accuracy, immunity to

electromagnetic influences and aggressive environments.

The fundamental principle behind OFS is the propagation of

light through an optical fiber cable (diameter of 125μm)

whose core is usually composed by silica (SiO2) and is

protected by an external polymer-type cladding. These can

further be protected by an extra coating layer despite the

present paper displays results extracted with strictly bare

OFSs. The light travelling through the core is a

monochromatic laser and moves forwards in the fiber thanks

to internal reflections. When light is travelling in the

optically dense medium that is the core and strikes a

boundary at a particular angle (larger than the critical angle

of the boundary), the light experiences total internal

reflection and is, therefore, confined in the core. Any

variation that the structural surface is subject to is reproduced

in the fiber (bonded on it) causing a physical

modification/perturbation in its optical core. These

perturbations can be detected thanks to light scattering; a

phenomenon that naturally occurs whenever the light beams’

photons interact with the core’s inhomogenities generating a

second magnetic wave (scattering or return) that heads back

towards the light source (backscattering)7. The main back-

scattered spectral components include Raman, Brillouin and

Rayleigh. These are measured to identify strain and

temperature variations.

OFS can be categorized into three different groups:

grating-based sensors, interferometric sensors and

distributed sensors. Most OFSs, such as Fiber Bragg Grating

sensors (FBG)8 or Fabry-Perot sensors9, are discrete and can

only provide local measurements thus potentially omitting

important information in structural areas that are not

explicitly instrumented. Furthermore, analyzing a structure’s

global behavior by means of discrete sensors would require

the installation of a high number of sensors producing a

dense system of monitored points, which translates into a

difficult and expensive deployment and complex data

acquisition. Distributed Optical Fiber Sensors (DOFS) were

developed to deal with these limitations allowing for a

distributed monitoring of strain and temperature along the

entire optical fiber length by means of a single cable between

the sensing fiber and the reading device. There are several

sensing technologies based on DOFS: Raman Optical Time-

Domain Reflectometer (OTDR), Brillouin Optical Time

Domain Reflectometer (BOTDR), Brillouin Optical Time

Domain Analysis (BOTDA), Optical Frequency Domain

Reflectometry (OFDR), Optical Backscatter Reflectometer

(OBR), among others. These are characterized by different

sensing ranges and spatial resolutions which makes them

suitable for different deployments. In particular, the OBR

technique used in the applications presented in this paper is

a Rayleigh Backscattering based Optical Backscatter

Reflectometer (OBR). It provides a good cost-efficiency

balance granting millimetric spatial resolutions at the

expense of low sensing range (only up to 70m10).

DOFS have been implemented in both laboratory

structural engineering experimental campaigns7,11,12 and in

real structural applications such as dams7,8, high rise

buildings13, bridges10,14, slopes15, piles16 and pipelines17

among others. However, given it is a new/under research

technology it still presents some limitations. To start its

elevated initial investment cost makes it a very selective

monitoring technique, the frequent appearance of anomalies

in the readings, the lack of reliable fiber-structure bonding

techniques and the lack of standardized guidelines that

ensure success in every deployment.

The frequent appearance of anomalies in the strain

measurements in the form of abnormally high peaks that

distort the strain profiles is the topic of the present article. In

our case, the article is aimed at proposing various numerical-

computing assisted methods for the identification and

treatment of such anomalous readings both novel and from

the literature. The Spectral Shift Quality method and

Geometrical Threshold Method are part of the latter category

while the Polynomial Interpolation Comparison Method is

introduced for the first time in the present article. Their

efficiency is tested on two study case scenarios; an

experimental laboratory campaign on two Reinforced

Concrete (RC) tensile elements (ties) and a real life in-situ

monitoring campaign of the inner surface of a lining-formed

metro tunnel in Barcelona. The results will testify the

efficiency of the novel methodology over the more

commonly used ones despite confirming the viability of the

latter for a fast preliminary analysis.

2 STRAIN READING ANOMALIES

Figure 1 below exemplifies the possible outputs of a strain

monitoring experimental campaign performed with the use

of DOFS. On the one hand, in Figure 1a the red plot displays

the deformation state of a 1.2m long DOFS over its multiple

points in the single instance in which the measurement is

performed. Such strain readings are assumed equivalent to

the one of the monitored surface on which it is bonded but in

reality it is a function of the ratio between the stiffness of the

latter and the used adhesive. On the other hand, Figure 1b

displays the evolution of strains of a single monitoring point

of the fiber versus the test time. As visible, the gathered

output is provided to the tester as a raw data set with the

following components:

Length vector: representing each sensing point along the

fiber (henceforth defined as DOFS coordinates) where

the measurements have taken place as a function of the

selected gauge length and gauge spacing or spatial

resolution.

Strain matrix: comprising the strain readings along the

whole fiber for a particular time in each row.

Time vector: specifying the date and time of the

performed measurement.

What is also evident in Figure 1a is the great clarity

difference between the red dashed and blue continuous plots.

This is due to the post-processing process that the blue curve

received in order to remove the visible large strain peaks

present in the DOFS raw output. These strain peaks, also

present in Figure 1b, are unexpectedly high, punctual in

nature and of doubtful meaning henceforth referred to as

Strain Reading Anomalies (SRAs).

Many DOFS monitored campaign report such anomalies.

In Villalba et al.7 the external face of a RC slab was

instrumented with DOFS in ordered to explore the fiber’s

crack detection ability. Here, large peaks are detected early

in the test and are attributed to points of strain concentration

due to cracks. As the load increases such peaks degenerates

into quasi-infinite peaks, clear SRA identifier. A DOFS

monitoring of another RC slab18 also reports SRAs. In Davis

et al.11 the strains inside different RC ties are monitored with

the goal of gaining insights into the concrete-reinforcement

bond performance of corroded specimens and the detection

of pitting corrosion. During the tension of the ties numerous

large peaks appear sometimes even deeply in compressive

domain which is improbable considering the nature of the

tensile test. Another RC tie test developed by the authors also

displayed the rise of SRAs with load12.

(a) (b)

Figure 1. DOFS-extracted strains profiles versus DOFS coordinates (a) and versus time (b)

In Barrias et al.19 the DOFS sensors were, instead, used to

monitor the deformations of a RC bending element unloaded

and reloaded again to assess the performance of the sensor

when applied to a real loading scenarios in concrete

structures. Here too, after the development of cracks, high

magnitude peaks are observed and later substituted through

interpolation with the surrounding values. These issues are

also present in other RC beams strain monitoring

campaigns20,21,22. Reported in-situ SHM campaigns are also

not SRA free23. These issues don’t seem to be isolated to

cases with RC though. Indeed, in Bado et al.24 a DOFS

monitoring campaign was performed on bending rebars

finalized to the analysis on the possible causes of the rise of

SRAs. Anomalistic readings were recorded beyond 4000με

and the authors concluded that, for strains inferior to such

level, the most probable cause of such anomalistic behavior

is the concrete’s friction (especially when cracked) against

the fiber.

Another possible reason for the appearance of such

anomalies is offered in Ding et al.25, suggesting that they are

caused by a localized failure of the algorithm that tracks the

light impulses through the range length under analysis and

during a particular wavelength sweep. Finally, it should be

noted that some deployments of DOFS sees the fiber being

bonded to or with highly heterogeneous materials (for

example, concrete), whose structural discontinuities (joints,

cracks, corners, etc.) may significantly affect the readings.

Generally talking, a strain peak at a DOFS coordinate xk

is usually considered as an abnormal reading if it presents a

large difference with previous reading at coordinate xk-1. This

is valid both in terms of time and space (time vector and

length vector). Temporally speaking, two consecutive

measurements should present similar strain readings when

the time interval between them, and thus their load

difference, is almost negligible. Spatially wise, if to consider

that the resolution of both experimental tests ranges between

5 and 10mm, strains simply hardly peak in neighboring

sections without a certain amount of lead-up gradual growth.

In some cases, opposite strain peaks in tension and

compression are reported in two neighboring readings which

is once again illogical given the short distances between the

two consecutive and theoretically similarly behaving

sections. A reading can be considered abnormal if large

tensile peaks appear in theoretically fully compressed area of

the structure or the other way around. All these reasons

suggest that these anomalies are reading errors from the

DOFS, fact that is confirmed in various experimental

campaigns19,24 that complemented the DOFS-monitoring

with other monitoring tools (strain gauges) and theoretical

models, which did not explain nor present the peaks read by

the DOFS.

In Bado et al.24 two types of strain-reading anomalies are

identified, harmful and harmless SRAs. The first, Harmless

Anomalies (HL-SRAs) are those strain peaks that, while

preventing the correct reading of the strains at a specific

time, still allows it in later instances. Being the nature of this

anomaly punctual in nature (see Figure 2), it is easily

identifiable in the strain profile of a section as an excessively

large and punctual peak surrounded by coherent strain

readings. Harmful Anomalies (HF-SRAs), are those strain

peaks that are followed strictly by additional anomalistic

readings.

Figure 2. Graphical representation of different SRAs’ theoretical definitions

Hence, from their initial appearance and for the rest of the

monitoring period, all the measurements are considered

unreliable. Figure 2 compares the looks of a DOFS reading

when affected by a HF-SRA at DOFS coordinate xk against

its neighboring sections (xk-1 and xk+1). Note that this kind of

anomalies might be “contagious”, meaning that the

surroundings of an identified HF anomaly might become, in

posterior times, an HF-SRA itself.

SRAs, combined with a lack of a universal reliable

DOFS/structural support bonding technique, limit DOFS

from becoming a reliable universal strain-reading tool. As a

result, SRAs prevent accurate and reliable readings (in a

specific location or along time), extensively increase the

level of unreliability of the surrounding measurements and

distort the global and/or local strain trends. In any DOFS-

monitored campaign these are crucial undermining factors

which may lead to the actual discarding of such technique.

Thus SRAs should be avoided entirely and, if that isn’t

possible, deleted in the data post-processing phase.

In order to identify all the anomalies in the readings, the

trend of every sensing DOFS section has to be studied and

each single anomalistic peak manually corrected and/or

removed. Such a tedious analysis may not actually be viable

in many projects considering factors such as large

dimensions of the data sets due to wide extensions of

monitoring surfaces or long monitoring periods, time-

limitations, financial constraints, lack of qualified personnel

and more.

With an essential contribution from computer

technology these issues can be tackled finally making DOFS

a viable performant option for any Structural Health

Monitoring campaign. Consequently, the need to develop an

algorithm that automatizes this process to the maximum

extent possible. The present paper proposes a post-

processing method aimed at achieving just that. In the

following chapters the logical process of the algorithm will

first be explained and later tested on the readings obtained

in two study case scenarios.

3 STUDY CASE SCENARIOS

This paper analyses the results of two different DOFS-

monitored deployments. The first is a structural laboratory

experimental campaign while the second is a real-life

application in a metro tunnel in Barcelona (Spain). In both

cases the monitoring was performed by means of an ODiSI-

A (Optical Distributed Sensor Interrogator) OBR (Optical

Backscatter Reflectometer) manufactured by LUNA

Technologies26. The ODiSI-A uses swept-wavelength

coherent interferometry to measure temperature and strains.

It offers the possibility to test a structure wholly or in the

chosen points of interest with user-configurable sensing

resolution and gauge lengths.

The laboratory experiment saw the DOFS instrumenting

of two RC ties named 12x12_D12.01 and 12x12_D12.02.

The first part is indicative of the cross-sectional dimension

of the RC tie (in our case 12cm tall and 12cm wide) whilst

the digits following the letter D are representative of the

rebar diameter (12mm). Their longitudinal dimensions are,

instead, displayed in Figure 3a. Whilst member

12x12_D12.01 is constituted of a single prism,

12x12_D12.02 is constituted of two concrete prisms that act

completely independently due to the tensile nature of the test

itself. Thus, by means of the resulting uniformous

distribution of stresses along the rebar during such test, this

layout allows the simultaneous but separate study of two RC

ties. The averaged concrete’s compressive strength is equals

to fcm= 39.5MPa, its tensile strength to fctm= 3.1MPa whilst

the two modulus of elasticity are Ecm=32.8GPa for concrete

and Esm=200.4GPa for steel. The DOFS is bonded to the

steel rebars in order to constantly monitor its strains when

subjected to monotonic tensile load through a Universal

Testing Machine (UTM) at a constant loading speed of

0.1mm/min. The 1.2m long fibers measured the steel’s

strains with a spatial resolution of 5mm and 7.5mm and were

bonded to them with cyanoacrylate (CYN) adhesive only

after it was positioned in a longitudinal groove that was

previously incised along the bar’s rib as in Figure 3b.

(a) (b)

Figure 3. Study case RC ties (a) with dimensional and

DOFS bonding characterization (b)

Figure 1 above displayed two DOFS strain measurements

extracted by the first of these two RC ties. As visible, despite

considering just one strain-DOFS coordinates and one

strain-time plot, numerous anomalies are already visible

requiring a hefty hand of post-processing.

(b)

(c)

(b)

(a) (c)

Figure 4. Tunnel DOFS installation (a), picture of the DOFS coordinates ~45.50m (b) and picture of DOFS coordinates from

~20-26m (c)

The in-situ DOFS deployment consisted in the monitoring

of the strains in Barcelona’s L9 Metro Sagrera TAV-Gorg

metro tunnels’ inner surface whose structural performance

could have been potentially affected by a residential building

being constructed on top and slightly covering its layout.

COTCA S.A. proposed a DOFS deployment in order to

perform a continuous follow-up of the tunnel’s strain and

tensional states during the excavation and construction

works happening 14.40m above the tunnel’s keystone.

The monitoring scheme involved the installation of a

50m long DOFS bonded to the concrete lining’s inner

surface (Figure 4) by means of epoxy resin after a previous

superficial preparation of the concrete lining that consisted

of, firstly, refining the surface’s existing irregularities with

sandpaper and, later, applying rubbing alcohol and special

products to avoid grease, air humidity and direct moisture.

Obviously, as with any real world application scenario

the installation conditions weren’t the best and the presence

of physical discontinuities could not be avoided. These

limitations might lead to a wide range of anomalies in the

readings which emphasizes the need for an appropriate post-

processing technique. The DOFS setup provided strain

readings with a spatial resolution of 10mm and was installed

along the supposedly most affected tunnel section, i.e. the

one found right below the construction site. Figure 4 shows

how, starting from the end, the fiber covers a complete

transversal section (coordinates 50.00m-23.00m), followed

by a longitudinal monitoring segment (23.00m-14.24m) and

ending in a partial transversal section coverage (14.24m-

10.00m). The remaining 10m are not bonded to any

structural surface and their main goal is aimed at providing

sufficient data to perform a temperature compensation of the

strain readings in case of variations during the monitoring

period.

Figure 5a presents the OBR strain measurement of a

single fiber coordinate at different instances during the

construction period (from October to May) in the DOFS

coordinates interval between 26 and 40m (for clarity purpose

the latter was chosen as it is the most representative of the

various kinds of SRA), as well as the delimitation of the

structurally differentiable segments that the fiber covers,

which, helps understand why some areas present a higher

amount of anomalies than others.

Figure 5b expands on Figure 5a by combining in a 3D

graph the un-processed DOFS strain measurements

collected in an exemplary 40-days span. This figure

summarizes the above explained SRAs as it clearly displays

how HF-SRAs, after their formation, remain present for the

rest of the monitoring campaign and how HL-SRAs quickly

appear and disappear. Furthermore, both anomalies can be

found in both tension and compression hence the strain

peaks can be identified on both sides of the graph.

Figure 5c zooms in Figure 5b in order to display, in

combination with Figure 5d, the difference between a HF-

SRA and a damage-induced peak where a crack appears

(both figures display the strain profiles of a 0.5m long DOFS

segment). As mentioned earlier, it is crucial not to confuse

the two as the unintentional deletion of the latter would go

against the purpose of the test itself. Granted HF-SRAs are

a consistent discontinuity against neighboring data, their

appearance due to damage in a RC structure is never

perfectly punctual. Oppositely, the presence of a certain

amount of strain build-up on both sides of a crack can always

be detected. This is evident in Figure 5d which displays a

three dimensional view of a DOFS strain monitoring

campaign (originally reported in Bado et al.12) of a Ø12 steel

rebar embedded inside a 100x100mm cross-sectional,

600mm long concrete prism and later tested in tension. In

the present figure it is possible to see two successive cracks

opening respectively at time 110s around DOFS coordinate

0.755m and time 217s in DOFS coordinate 0.94m. Figure

5d’s results are similar to other DOFS monitoring

campaigns’ performed both on the external surface of a RC

member7,27 and inside it (DOFS bonded to rebars)28,29. As a

matter of fact, in these campaigns the adjacent build-ups can

assume the aspect of an inverted nosecone cross-section

whose base is as small as 20cm and as large as half a meter.

This non-abrupt but relatively gradual rise in strains allows

to clearly distinguish the insurgence of a damage in the

structure against a HF-SRA.

The significantly different nature of this paper’s study

case deployments allows for the development of a general

and widely applicable post-processing technique on the

basis of their collected readings.

4 THE SRAS POST-PROCESSING STEPS

The objective of a post-processing algorithm is to treat the

raw strain measurements and obtain a new set of data that is

more reliable and as free as possible of any SRAs-induced

distortion. Its core process is based on the following logical

sequence.

1. 𝐴𝑢𝑡𝑜𝑚𝑎𝑡𝑖𝑐 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑆𝑅𝐴𝑠 → 2. 𝑅𝑒𝑚𝑜𝑣𝑎𝑙 𝑜𝑓 𝑆𝑅𝐴𝑠

→ 3. 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 𝑏𝑦 𝑖𝑛𝑡𝑒𝑟𝑝𝑜𝑙𝑎𝑡𝑖𝑜𝑛

The automatic detection of the SRAs is the most crucial part

of the process. Being HL-SRAs effectively data outliers,

commonly one would label a data as a potential outlier when

the latter’s standard deviation surpasses by a certain number

of folds (usually 2) the mean. Yet, the presence of outliers is

likely to have a strong effect on the mean and the standard

deviation themselves thus making this technique

pragmatically defective. Elsewise, an outlier reading can be

considered as any value that is more than three scaled

median absolute deviation (MAD) away from the median

value within a sliding window. Still this method wouldn’t

meet the necessary requirements for detecting an SRA as it

wouldn’t be able to distinguish an SRA from a strain peak

caused by a sudden opening of a crack, impact or load

increase effectively removing the data indiscriminately.

Furthermore, this method would be unable to detect HF-

SRAs due to the proximity of erroneous strain values

subsequent to the first anomalistic reading. As a matter of

fact, no post-processing should be run without a previous

thoughtful review of the loading and structural conditions of

the case study one is working on. Indeed, being the objective

the deletion of unreliable readings that do not reflect the real

behavior of the monitored structure, care should be taken in

the coherence of the peaks elimination. It should be neither

excessive (which would imply a loss of reliable data) nor

insufficient (which wouldn’t allow for interpretation of

readings).

For example, as mentioned earlier, if a laboratory

experiment involves the evaluation of a structure under

impact loading or up until crack formation, a correct post-

processing would have to account for a sudden and high

strain variation between consecutive readings. Thus, the

tendency of the raw data should be first identified and only

later can the peaks elimination pattern be defined.

Just as the strain matrix can be referred to the length

vector or the time vector so can the detection of SRAs be

performed along space or time. SRAs in space and time are

exemplified in Figure 6. Notice that the HL and HF-SRAs

displayed in Figure 2 are actually jumps in time. Anomalies

in space are usually of the HL kind hence only appear as a

single large peak. An abrupt increase of strain magnitude

which remains constant thereafter (looking like a HF

anomaly) could happen, for example, if a single fiber is used

to continuously monitor differently stressed structural

surfaces (a beam in bending with the fiber bonded

sequentially on the upper and lower surfaces for instance).

In the current study cases, though, such condition isn’t met

as the fiber is uniquely and continuously bonded to a rebar

(for the RC tie case) and the inner tunnel’s ring surface.

The present paper intends to outline two SRAs

identification methods used in literature and a novel

polynomial based method. Their algorithms will be

displayed in later chapters, for the present moment the

elimination and substitution steps will be dealt with (and

their algorithm displayed) with a conforming simplification.

(a)

(b)

(c) (d)

Figure 5. Multiple (a) and all (b) tunnel strain measurements along the monitoring duration (c) with a zoomed section showing

the appearance of a HF-SRA (d) compared against the appearance of damage (cracking) in a RC element

Figure 6. Strain anomalies detection versus DOFS coordinates (space) and time

Once the SRAs have been detected the next step is their

elimination. Hence, all the detected anomalies are

substituted with a NaN value (which stands for “Not a

Number”) as in the flowchart in Figure 7.

Figure 7. Idea behind the detection of SRAs

NaN (or #N/A) is a numeric data type used by a computing

software that represents an undefined or unrepresentative

value. As visible later, according to different SRAs detection

techniques, specific algorithms are developed for such

eliminations. In order to replace the NaN values with correct

interpolation substitutes, there are two distinct kinds of

interpolation; time and space interpolation which correct

their respectively located SRAs. Once again, space

interpolation is the only way to delete HF-SRAs. In the strain

matrix organization, rows represent the strains along the

fiber at particular times, and columns the strain evolution in

time of each monitored point. The interpolation algorithm

goes through each row or each column looking for the NaN

readings and substituting them with an interpolation of the

first surrounding reliable strain readings. In order to achieve

such when there are multiple NaN readings in a row, the

algorithm uses an auxiliary variable k (see algorithm in

Figure 8) which starts counting how many anomalies follow

it.

When the first non-anomalous reading appears, the counter

k stops indicating the index distance at which the algorithm

should pick the strain value to interpolate the first one with

(the one before the NaN).

Together these two enable the computation of the

interpolated values between them (Figure 8). Indeed, the

algorithm is constituted of two parts of which the first

actively “looks” for NaN value in the matrix and the second

“looks” for the correct values to achieve the interpolation. If

the SRA detection algorithm is performant enough, through

the correct substitution of all NaN values, a fully improved

and SRA free strain matrix is finally achieved.

5 POST-PROCESSING METHODS

With the logical steps of the algorithm in mind the present

paper intends to outline two SRAs identification (and

consequent cleaning) methods used in literature with

different levels of sophistication (thus leading to results of

variable quality) and a novel polynomial based method.

5.1 Strain Shift Quality (SSQ) method

Besides strain and temperature readings, the ODiSI-A OBR

allows for the computation of the Spectral Shift Quality

(SSQ) of each reading. The SSQ is described by the

provider26, as a measure of the reliability of the

corresponding readings by measuring the level of the

correlation between the measurement and baseline reflected

spectra as in Equation 1 below.

𝑆𝑆𝑄 =𝑚𝑎𝑥 (𝑈𝑗(𝑣) ∗ 𝑈𝑗(𝑣 − ∆𝑣𝑗))

∑ 𝑈𝑗(𝑣)2 (1)

where:

𝑈𝑗(𝑣) is the baseline spectrum for a given segment of data

𝑈𝑗(𝑣 − ∆𝑣𝑗) is the measurement spectrum under a strain

or temperature variation

∗ is the cross-correlation operator

In other words, it is a function that determines the

quality/reliability of a strain reading by correlating the

original baseline measurement and the measurement spectra

normalized by the maximum expected value.

Figure 8. General SRA substitution algorithm

According to its definition, the SSQ value remains between

0 and 1, where 1 translates into a perfect correlation and 0

into an uncorrelated value. The provider states that the data

sets are accurate if the SSQ is higher than 0.15 meanwhile,

if it is lower, it is very likely that the read strain or

temperature has exceeded the measurable range.

In this investigation, the SSQ function is proposed and

assessed as a tool for SRAs identification by establishing a

minimum SSQ value, or SSQ threshold, with which one can

invalidate a percentage of SRAs. The minimum/optimal

SSQ threshold that allows for the deletion of the highest

percentage of SRAs while producing a physically

interpretable set of data is a case by case and trial and error

matter. Its only constraint is that it has to be above 0.15 (as

recommended by the ODiSI software manufacturer). Figure

9 depicts the algorithm required to perform an SSQ data

post/processing.

This algorithm requires as input data the strain and SSQ

matrices provided directly by the sensing software and an

SSQ threshold below which the respective strain readings

will be considered as anomalistic and removed. As

explained above, the output is a new strain matrix with

missing data (NaN) replacing the identified anomalies.

Figure 10 illustrates the strains measured in DOFS

section 1.0425m of the laboratory test’s member

12x12_D12.01 at different time steps (not seconds) along

with each measurement’s relative SSQ value.

What is visible is, first of all, that no clear variation of

the SSQ value is present in correspondence to the abnormal

strain peaks (HL-SRAs). Secondly, that it is not uncommon

that the SSQ value instead of decreasing in correspondence

to the SRAs, it actually increases thus misleading the reader

into thinking that those are of the same if not higher quality

measurements.

Lastly the value of the SSQ seems to oscillate in quality

even in intervals where only good strain measurements are

being recorded. This complicates the task of setting an SSQ

threshold that distinguishes reliable and unreliable readings

thus increasing the risk of indiscriminately removing

reliable data along with unreliable ones.

Figure 9. SRAs detection and removal with an SSQ tool

Figure 10. DOFS strain measurements compared to their

SSQ

This is evident in Figure 11 which illustrates the outcome of

an SRA elimination according to different SSQ threshold

values (0.15, 0.25, 0.35 and 0.45) for the laboratory

members 12x12_D12.01 and 12x12_D12.02. The latter is

presented in three points in time or loading level differently

colored for clarity purposes.

The gradual decrease of the SRA peaks with the increase

of the SSQ threshold is clear but at the same time it is also

noticeable how, for higher ones the trend of originally SRA-

heavy segments (such as segment 1.087-1.185m for

12x12_D12.01 and 0.89-0.97m for 12x12_D12.02) is

distorted due to an excessively undiscerning points deletion.

Figure 11e exemplifies the case where the SSQ threshold is

so high that almost no point is considered reliable hence they

were all removed. In Figure 11a the SSQ method seems

more performant than in Figure 11b to d which is in line with

what was suggested above concerning the variability of the

results from case to case. Additionally, the SSQ threshold

that seems to work best for member 12x12_D12.01,

SSQ=0.35, is far from acceptable for member

12x12_D12.02 and vice versa. A universally efficient SRA

cleaning method should not perform in such aleatory way.

In conclusion despite the SSQ is a good tool to clear the

largest SRAs and clarifying the profile trend, it is an

excessively rough post-processing tool, unable to

consistently provide clean and reliable strain profiles

whenever medium/high levels of accuracy and precision

would be required.

5.2. Geometrical Threshold Method (GTM)

In order to identify the SRAs, their own definition could be

directly used. Indeed, being these strain readings sudden and

overly large, they imply a great variation between two

consecutive readings. On the ground of such, a maximum

strain variation (GT threshold) can be defined and used to

identify the appearance of an SRA. This method will be

henceforth referred to as Geometrical Threshold Method

(GTM). This SRAs identification process based on strain

‘jumps’ can be applied both temporally and spatially but is

unable to detect nor correct HF-SRA since, after the first

anomalistic reading, another very similar in magnitude

follows so whilst the first might be detected as an SRA, all

the following ones won’t. Thus this method can only be

considered as an HL-SRAs detection method. Figure 12

depicts the algorithm required to perform a GTM data

post/processing.

The presented algorithm shows the detection process of

strain jumps between consecutive readings (in time). As

mentioned before, the detection of jumps between nearby

readings might also be required, for that, an exchange of all

i and j in the routine would be enough. The possible presence

of missing readings in the input strain matrix is taken into

consideration to allow for the combination of different SRAs

removal routines.

(a)

Figure 11. 12x12_D12.01’s (a) and 12x12_D12.02’s (b) to (e) SSQ processed strain profiles through different SSQ thresholds

Figure 12. SRAs detection algorithm with a GTM tool

The strain increment (maxΔ) that identifies the SRA has to

be carefully chosen so as to avoid deleting correct jumps

(related to cracks or sudden load increments) and focus only

on the anomalistic jumps. Figure 13 below illustrates the

outcome of an SRA elimination according to different

thresholds (50, 150, 500 and 1000με). Figure 13b to e should

be compared with the original strains plotted in Figure 11b

Once again the removal of the largest SRAs is immediate

and the optimal geometrical threshold is for both members

50με. Once again though, the anomalies that were corrected

were strictly HL-SRAs in addition to a certain amount of

profile distortion in the SRAs heavy segments.

5.3. Polynomial Interpolation Comparison Method

(PICM)

The Polynomial Interpolation Comparison Method is a

routine based on the very simple concept of what is an error.

The core idea is based on the development of an

approximated polynomial curve of the study case DOFS

section’s ε-t profile which encompasses the maximum

number of reliable strain readings of the profile (effectively

representing its trend). The polynomial degree can vary to

provide improved fitting even though, generally talking, it

should be neither too low (which would lead to non-

representative tendencies), nor too high (because the trend

would in return be affected by the punctual anomalies).

As example, Figure 14 below represents different DOFS

sections of member 12x12_D12.02 with the original data

(thin blue) including clear anomalies, the selected

polynomial curve in red and finally the corrected data in

green. When the strain matrix includes SRAs of small

magnitude it is possible to automatically generate

polynomial fitting curve as in Figure 15a for the

experimental member 12x12_D12.01 and Figure 15b for the

DOFS tunnel deployment (approximation ε-t curve in red

and pink for two measuring points in critical locations).

Instead, when the strain matrix includes SRAs of high

magnitude, developing a trend line would be meaningless

since the amount of SRAs would affect its profile preventing

it from reflecting the real behavior of the section (as in

Figure 14a). In this case a manual defining and plotting of

the curve is possible. The DOFS strain curve is compared to

the polynomial approximation curve resulting in a certain

amount of error per measurement.

(a)

Figure 13. Member 12x12_D12.01’s (a) and 12x12_D12.02’s (b) to (e) strain profiles processed with the GTM method and

different maximum strain thresholds

Figure 14. Strain measurements along time of anomalistic DOFS sections versus their polynomial curve approximations (in

red) of member 12x12_D12.02

(a) (b)

Figure 15. SRAs detection with PICM of laboratory tests’ (a) and tunnel’s (b) readings when the SRAs’ magnitude is small

Following the definition of a maximal error between the two

curves’ points, whenever the error is higher than such

established limit, the reading is considered as an SRA. This

is achieved through a very simple function that checks the

difference between the reading and its corresponding

expected value (belonging to the ε-t curve approximation) as

in Equation 2:

𝐸𝑟𝑟𝑜𝑟𝑖 = |𝜀𝐷𝑂𝐹𝑆,𝑖 − 𝜀𝐴𝑃𝑅𝑂𝑋,𝑖|

𝑖𝑓 𝐸𝑟𝑟𝑜𝑟𝑖 > 𝐸𝑟𝑟𝑜𝑟𝑚𝑎𝑥 ⇒ 𝜀𝐷𝑂𝐹𝑆,𝑖 = 𝑆𝑅𝐴

𝑖𝑓 𝐸𝑟𝑟𝑜𝑟𝑖 ≤ 𝐸𝑟𝑟𝑜𝑟𝑚𝑎𝑥 ⇒ 𝜀𝐷𝑂𝐹𝑆,𝑖 ≠ 𝑆𝑅𝐴

(2)

The choice of the threshold value 𝐸𝑟𝑟𝑜𝑟𝑚𝑎𝑥 has to be, as

always, a result of an in-depth study of the measured

tendencies and peaks. Figure 16 depicts the algorithm

required to perform a PICM data post/processing. The latter

requires as input data the raw strain matrix, its previously

developed polynomial fit and a maximum error that is

accepted between them (maxError). The difference between

the matrices is computed and, when it exceeds the maximum

error, the polynomial fit matrix element substitutes the strain

matrix one. As mentioned for the GTM routine, the

maximum error has to be carefully defined to avoid the

removal of correct strain measurements.

Figure 16. SRAs detection algorithm with a PICM tool

(a) (b) (c)

Figure 17. Member 12x12_D12.02’s original strain profiles (a) processed with the PICM method (b) and finally the output (c)

Figure 1 displayed in red the outcome of a PICM post-

processing of one of the 12x12_D12.01 member’s DOFS

strain profiles. Expectedly all the peaks were removed

providing us with a clear and distinguishable outline.

Similarly, Figure 17 displays respectively the raw strain

profiles as extracted by the OBR from member

12x12_D12.02 at three points in time or loading level, a

representation of the stitching job performed by the post-

processing algorithm versus the original data and finally the

much improved SRA-free output.

It should be noted though that, as per the other methods,

in the presence of too many consecutive SRAs, their removal

and interpolation might lead to segments of the graph with a

higher degree of uncertainty. This is the case of the profile

corresponding to the bare segment of the rebar between the

two concrete blocks (0.89-0.97m). The same could be stated

for member 12x12_D12.01 for DOFS coordinates 1.095-

1.178m. Yet, thanks to this method’s ability to recognize

reliable values in between SRAs, the overall unreliability of

the PICM extracted profile is clearly inferior to the SSQ’s

and GTM’s.

6 POST-PROCESSING RESULTS OF REAL-LIFE

STUDY CASE SCENARIO

In the present chapter the above explained post-processing

algorithms are used to clear out the SRAs from the strain

matrix originated by the in-situ tunnel monitoring along 300

days.

The first adopted method is the SSQ. As can be seen in

the Figure 18b to d, different SSQ thresholds provide

different outcomes compared to the original strain data

represented in Figure 18a.

An obvious aspect of this figure is that the total amount of

SRAs decreases as the SSQ threshold increases. Despite still

presenting a significant amount of anomalies (in particular

HF-SRAs), the best fit (surrounded in red) can be achieved

after the removal of the measurements with associated SSQ

values lower than 0.30.A lower threshold, presents an

uninterpretable set of data due to an excessive amount of

SRAs, whilst a higher one translates into too many

measurements being deleted.

Despite the global trend can be distinguished, the graphs

are still plagued by enough SRAs to lead to interpretation

confusion which is detrimental when monitoring the need

for emergency maintenance into the tunnel. Thus, SSQ

cannot be considered a reliable post-processing method.

Passing on to GTM, when approaching an SHM

monitoring of a real case scenario with this post-processing

analysis, a lot of care should be taken when deciding the

threshold. Indeed, when the structure’s future behavior is

completely unknown to the engineer, it may suffer large

strains peaks (for example due to the appearance of cracks

or impacts) which might but should never be confused with

SRAs. This is particularly valid when DOFS are bonded to

the structure’s external structural surface (as seen in

literature23,19) as is the case for the present study scenario. In

this case a GTM analysis should be performed in the

direction where there are the least expected sudden strain

jumps; along space (along the DOFS coordinates). Thus,

assuming that in the present case the strains do not vary more

than 250με in less than 10mm (not even when cracking is

considered) the resulting GTM post-processing is

represented in Figure 19a.

Despite the actual size of the SRAs isn’t excessive, their

disproportionate amount still present in the post-processed

surface plot implies the poor performance of GTM as a post-

processing tool for an in-situ superficial monitoring. Even

when lowering the Geometrical Threshold to 50με (Figure

19b) a large number of anomalies would still be present.

Moving on to the PICM analysis, given the original data

matrix (plotted in Figure 20a), the best polynomial fit is

calculated for the evolution of the strains in each DOFS

coordinate along time (as exemplified by Figure 15b) which,

combined together, provide the polynomial fit represented in

Figure 20b. Despite not being composed of actual measured

points, Figure 20b already provides a good feeling of the

strain evolution in each segment of the tunnel.

(a)

(b) (c) (d)

Figure 18. DOFS-extracted strain measurements of segment 10-50m (a) and the result of SSQ post-processing for different

SSQ thresholds (b) to (d)

When finally developing a PICM comparative fit between

the original data (Figure 20a) and its extracted trend-lines

(surface in Figure 20b), the post-processed output of the

strain matrix (Figure 20c) is a much improved surface plot

compared to its original state. Indeed, having been the

largest amount of SRAs successfully eliminated, the layout

is immediately clearer and strictly composed by actual

DOFS reliable measurements.

7 POST-PROCESSING METHODS COMPARISON

In the previous sections the inner workings of each post-

processing algorithm were discussed along with a look at

their performance. A final comparison amongst these is

presented in the following by putting side to side strictly the

output of the analysis that performed best (in case of SSQ

and GTM the thresholds that provided the highest amount

of SRAs correction) for each post-processing method.

Figure 21 below summarizes the latter by collecting the

plots whose parameters provide the best fit to the reliable

points of the original DOFS extracted strain profiles for

member 12x12_D12.01 and 12x12_D12.02.

For members 12x12_D12.01 and 12x12_D12.02 their

respective SSQ thresholds are 0.35 and 0.25 whilst their

selected GTs’ is 50με for both. Figure 21 shows how for all

diagrams removing the HL-SRAs provides a relatively

trust-worthy diagram. For member 12x12_D12.01, the only

method that not only takes advantage of all the reliable

points to plot the graph but also extracts a somewhat

symmetrical profile is the PICM method.

(a) (b)

Figure 19. GTM post-processed DOFS-extracted strain measurements for a geometrical threshold of 250με (a) and 50με (b)

(a) (b)

(c)

Figure 20. Original DOFS extracted strain evolution in time (a) which, when combined with a polynomial fit (b), results in

PICM processed output (c)

12x12_12.01 12x12_D12.02

Figure 21. SRA-cleaning post-processing methods comparisons for member 12x12_D12.01 (a) to (d) and 12x12_D12.02 (e)

and (f)

(a) (b) (c) (d)

Figure 22. SRA-cleaning post-processing methods comparisons (SSQ (b), GTM (c) and PICM (d)) for the in-situ tunnel

monitoring versus the original strains (a)

Oppositely, SSQ and GTM (the former more than the

latter) undiscriminatingly removed the data in the right

branch of the graph thus giving it a false inclination that does

not envelop nor represent the points there present. The strain

profiles of member 12x12_D12.02 are quite rectilinear, thus

decisively compatible with a rougher anomalistic detection

and removal method such as SSQ and GTM. For this reason,

the profile extracted from these methods are quite similar to

PICM´s in Figure 21f.

Moving on to the tunnel monitoring, once again PICM

seems to be the method that provides the best results as can

be seen in Figure 22. As a matter of fact, almost all SRAs

are removed whilst in the other two cases only partially. As

proven by the SSQ and GTM results, HF-SRAs is the kind

of anomaly that proves to be the hardest to remove due to its

hard detection. Despite such, PICM successfully proceeds to

eliminate these too.

In conclusion, considering both the post-processing

results extracted from the laboratory RC ties test and the

tunnel monitoring, the most consistently reliable method is

PICM as it delivered trust-worthy mostly-SRA-free strain

profiles for both. This should definitely be the preferable

post-processing technique for monitoring cases where

precision is a hard requirement such as laboratory work and

detailed analysis aimed at taking important intervention

decisions (such as the case of the in-situ monitoring). As

previously suggested the SSQ and GTM methods are faster

and simpler but cruder post-processing approaches adapt

only for quick and general checks.

A Strengths Weaknesses Opportunities Threats (SWOT)

graph encapsulating all of the previous points is suggested

in Table I. It summarizes the advantages and disadvantages

of each post-processing method thus helping in the choice of

most fitting method for different applications.

Table I. Strengths Weaknesses Opportunities Threats (SWOT) graph

STRENGTHS WEAKNESSES

SSQ - Low computational cost thus speed

- largest SRAs treatment

- Roughly clarifies global trend

- No consistent correlation between anomalies and SSQ values

- Complicated SSQ threshold setting

- High risk of indiscriminately removing reliable data along with SRAs

GTM

- Medium computational cost thus speed

- Based on anomalies’ definition - Able to detect HL SRAs

- Unable to detect HF SRAs

- Complicated jump threshold setting - Profile distorts in SRAs heavy segments

PICM

- Based on simple error concept

- Able to detect both HL & HF SRAs

- Provides clear, distinguishable and physically interpretable outline

- High computational cost - Not fully automatized as it requires manual fitting in

SRAs heavy segments.

OPPORTUNITIES THREATS

SSQ - SSQ values are computed by the OBR itself thus

providing quick results

- High risk of misinterpretation of the extracted data - Poor efficiency for non-linear loading processes and

strain profiles

GTM - Works well with linear/monotonic loading

processes and strain profiles

- Misinterpretation of the extracted data - Inadverted removal of crucial data such as damage peaks

- Non-linear loading processes and strain profiles

PICM

- Efficiency does not depend on loading processes nor strain profile shape

- Works well both for a controlled and monitored

environment (lab test) and uncertainly behaving structures (real-life applications).

- High computational and time cost may lead to a delay in the detection of alarming structural deformation/damage

8 CONCLUSIONS

Despite Distributed Optical Fiber Sensors (DOFS) hold

huge advantages over classic civil engineering strain

monitoring tools, their applicability is limited by sudden

disruptive strain reading anomalies (SRAs) that seem to be

inherent to the measuring principle of backscattering taking

place in DOFS. These unreliable points usually take the form

of large, out of scale strain peaks or isolated drastic upsurge

of strain order of magnitude. These anomalies aren’t

necessarily deal breaking as the DOFS extracted data can be

treated with a process of SRA detection, elimination and

finally substitution. The present paper discussed different

ways of performing these tasks. The core algorithm of two

methods previously used in literature (Spectral Shift Quality

and Geometrical Threshold Method) and of a novel

polynomial based one (Polynomial Interpolation

Comparison Method) was shown and applied to two study

case scenarios in order to test their performance. These two

scenarios were an experimental laboratory test on two

Reinforced Concrete (RC) tensile elements (ties) and an in-

situ metro tunnel monitoring campaign. The resulting

outputs showed the ability of each of these methods to

remove the erroneous and damaging strain readings despite

large performance discrepancies. Indeed, despite providing

a quick and small computational taxing analysis, the classic

methods (SSQ and GTM) were not able to clear out all SRAs

in the case of the tunnel monitoring and provided relatively

distorted strain profiles in the case of the two RC ties. The

novel polynomial based strain interpolation method (PICM),

instead, provided output plots free of any strain peak and

with the minimum amount of distortion for both. As a result,

the latter is identified as the best SRA cleaning post-

processing method when accurate and reliable measurement

are required.

ACKNOWLEDGMENTS

The study was performed within project No 09.3.3-LMT-K-

712-01-0145 that has received funding from European

Social Fund under grant agreement with the Research

Council of Lithuania (LMTLT). Furthermore, the authors

acknowledge the help of COTCA Asistencia Técnica,

Patología y Control de Calidad for the contribution provided

in lending the OBR ODiSI-A machine and to TMB

(Barcelona Transport Authority) for giving access to the

monitored data of the metro tunnel.

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(a) (b)

Figure 1. DOFS-extracted strains profiles versus DOFS coordinates (a) and versus time (b)

300x300 DPI

Figure 2. Graphical representation of different SRAs’ theoretical definitions

300x300 DPI

(a) (b)

Figure 3. Study case RC ties (a) with dimensional and DOFS bonding characterization (b)

300x300 DPI

(b)

(c)

(b)

(a) (c)

Figure 4. Tunnel DOFS installation (a), picture of the DOFS coordinates ~45.50m (b) and picture of DOFS coordinates from

~20-26m (c)

300x300 DPI

(a)

(b)

(c) (d)

Figure 5. Multiple (a) and all (b) tunnel strain measurements along the monitoring duration (c) with a zoomed section showing

the appearance of a HF-SRA (d) compared against the appearance of damage (cracking) in a RC element

300x300 DPI

Figure 6. Strain anomalies detection versus DOFS coordinates (space) and time

300x300 DPI

Figure 7. Idea behind the detection of SRAs

Vectorial image

Figure 8. General SRA substitution algorithm

Vectorial image

Figure 9. SRAs detection and removal with an SSQ tool

Vectorial image

Figure 10. DOFS strain measurements compared to their SSQ

300x300 DPI

(a)

Figure 11. 12x12_D12.01’s (a) and 12x12_D12.02’s (b) to (e) SSQ processed strain profiles through different SSQ thresholds

300x300 DPI and Vectorial image

Figure 12. SRAs detection algorithm with a GTM tool

Vectorial image

(a)

Figure 13. Member 12x12_D12.01’s (a) and 12x12_D12.02’s (b) to (e) strain profiles processed with the GTM method and

different maximum strain thresholds

300x300 DPI and Vectorial image

Figure 14. Strain measurements along time of anomalistic DOFS sections versus their polynomial curve approximations (in

red) of member 12x12_D12.02

Vectorial image

(a) (b)

Figure 15. SRAs detection with PICM of laboratory tests’ (a) and tunnel’s (b) readings when the SRAs’ magnitude is small

Vectorial image and 300x300 DPI

Figure 16. SRAs detection algorithm with a PICM tool

Vectorial image

(a) (b) (c)

Figure 17. Member 12x12_D12.02’s original strain profiles (a) processed with the PICM method (b) and finally the output (c)

Vectorial image

(a)

(b) (c) (d)

Figure 18. DOFS-extracted strain measurements of segment 10-50m (a) and the result of SSQ post-processing for different

SSQ thresholds (b) to (d)

300x300 DPI

(a) (b)

Figure 19. GTM post-processed DOFS-extracted strain measurements for a geometrical threshold of 250με (a) and 50με (b)

300x300 DPI

(a) (b)

(c)

Figure 20. Original DOFS extracted strain evolution in time (a) which, when combined with a polynomial fit (b), results in

PICM processed output (c)

300x300 DPI

Figure 21. SRA-cleaning post-processing methods comparisons for member 12x12_D12.01 (a) to (d) and 12x12_D12.02 (e)

and (f)

Vectorial image

(a) (b) (c) (d)

Figure 22. SRA-cleaning post-processing methods comparisons (SSQ (b), GTM (c) and PICM (d)) for the in-situ tunnel

monitoring versus the original strains (a)

300x300 DPI